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Far-infrared reflectance of a MgB2 film has been measured by Fourier-transform spectroscopy for frequencies 10 cm^{-1}<\nu <4000 cm^{-1} above and below the superconducting transition. The data provide clear experimental evidence for the onset of a superconducting gap at 24 cm^{-1} at T=5 K. On increasing temperature the gap energy increases, contrary to what is expected in isotropic BCS superconductors. The small zero-temperature gap value and its unconventional increases on increasing temperature can only be explained by a highly anisotropic or multiple gap function.

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